Single-copy entanglement in a gapped quantum spin chain

TL;DR

This paper demonstrates that in a gapped quantum spin chain, specifically the AKLT model, the single-copy entanglement equals the von Neumann entropy, indicating all entanglement can be extracted from a single system.

Contribution

It establishes that for the AKLT gapped spin chain, the single-copy entanglement matches the von Neumann entropy, revealing a fundamental property of entanglement in gapped systems.

Findings

Single-copy entanglement equals von Neumann entropy in the AKLT chain.

All entanglement in the AKLT chain can be distilled from a single specimen.

Contrasts with critical chains where single-copy entanglement is half the von Neumann entropy.

Abstract

The single-copy entanglement of a given many-body system is defined [J. Eisert and M. Cramer, Phys. Rev. A. 72, 042112 (2005)] as the maximal entanglement deterministically distillable from a bipartition of a single specimen of that system. For critical (gapless) spin chains, it was recently shown that this is exactly half the von Neumann entropy [R. Orus, J. I. Latorre, J. Eisert, and M. Cramer, Phys. Rev. A 73, 060303(R) (2006)], itself defined as the entanglement distillable in the asymptotic limit: i.e. given an infinite number of copies of the system. It is an open question as to what the equivalent behaviour for gapped systems is. In this paper, I show that for the paradigmatic spin-S Affleck-Kennedy-Lieb-Tasaki chain (the archetypal gapped chain), the single-copy entanglement is equal to the von Neumann entropy: i.e. all the entanglement present may be distilled from a single specimen.